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When writing proofs by contradiction we begin by assuming the opposite of a statement, and then show that this leads to (i.e. entails) a contradiction. Which of the following statements constitutes a contradiction (that is, which of the ollowing evaluates to false)? Suppose A and B to be sets of natural numbers, and r to be a natural numbers. Select all that apply. A. O (x E A) A (x e B) ^ (An B = 0) B. O (x E B) → (x E A) → (2 € B)) ) ^ (x € A) C.O (r E A) A (x e B) ^ (x ¢ (AU B)) D. O (x € A) ^ (x ¢ B) ^ (x € (AN B)) E. O None of the above

When writing proofs by contradiction we begin by assuming the opposite of a statement, and then show that this leads to (i.e. entails) a contradiction. Which of the following statements constitutes a contradiction (that is, which of the ollowing evaluates to false)? Suppose A and B to be sets of natural numbers, and r to be a natural numbers. Select all that apply. A. O (x E A) A (x e B) ^ (An B = 0) B. O (x E B) → (x E A) → (2 € B)) ) ^ (x € A) C.O (r E A) A (x e B) ^ (x ¢ (AU B)) D. O (x € A) ^ (x ¢ B) ^ (x € (AN B)) E. O None of the above

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.2: Solving Inequalities
Problem 51WE
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When writing proofs by contradiction we begin by assuming the opposite of a statement, and then show that this leads to (i.e. entails) a contradiction. Which of the following statements constitutes a contradiction (that is, which of the following evaluates to false)? Suppose A and B to be sets of natural numbers, and æ to be a natural numbers. Select all that apply. A. O (x E A) A (x e B) A (An B = 0) B. O ( (x E B) → ((x E A) → (a e B)) ) A (x E A) C.O (* E A) A (æ € B) ^ (x ¢ (AU B)) D. O (* E A) A (r ¢ B) ^ (x E (A n B)) E. O None of the above
Transcribed Image Text:When writing proofs by contradiction we begin by assuming the opposite of a statement, and then show that this leads to (i.e. entails) a contradiction. Which of the following statements constitutes a contradiction (that is, which of the following evaluates to false)? Suppose A and B to be sets of natural numbers, and æ to be a natural numbers. Select all that apply. A. O (x E A) A (x e B) A (An B = 0) B. O ( (x E B) → ((x E A) → (a e B)) ) A (x E A) C.O (* E A) A (æ € B) ^ (x ¢ (AU B)) D. O (* E A) A (r ¢ B) ^ (x E (A n B)) E. O None of the above
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